What is the sum of an 8-term geometric sequence if the first term is 10 and the last term is 781,250? I know n=8, a1=10, an=781,250.
I just don't understand how to find the common ratio if a list of the terms is not given and the problem doesn't say what the common ratio is?

Question

What is the sum of an 8-term geometric sequence if the first term is 10 and the last term is 781,250?	I know n=8, a1=10, an=781,250. 
I just don't understand how to find the common ratio if a list of the terms is not given and the problem doesn't say what the common ratio is?

campbell_st · Answer

a term in a geometric sequence is found using

$$T _{n} = ar^{n -1}$$

in your question you have the 8th term, the 1st term and n

$$781250 = 10 \times r^{8-1}$$

then 

$$r^7 = 78125$$

$$r = \sqrt[7]{78125} = 5$$

now you can find the sum

anonymous · Answer

So the ratio is 5?